1. Notes 2 ECE 2317 Applied Electricity and Magnetism Prof. D. Wilton
ECE Dept.
Charge!
Notes 2
Notes prepared by the EM group, University of Houston.

2. Statics Definitions: Statics – frequency f = 0 [Hz]
Quasi-statics – slow time variation, f << ? [Hz]
The electromagnetic field splits into two independent parts:
Electrostatics: (q, E) Static charge
Magnetostatics: (I, B) Constant current w.r.t. time

3. Statics (cont.)
Example:
circuit

4. Statics (cont.) c = 2.99792458  108 [m/s] Example: f = 60 [Hz]
0 = c / f
c =  108 [m/s]
f = 60 [Hz]
This gives: 0 = 106 [m]
= 4,996.5 [km]
= 3,097.8 [miles]
Clearly, most circuits fall into the static-approximation category at 60 [Hz]!

5. Statics (cont.)
The following rely on electro(quasi-)static and magneto(quasi-)static field theory:
circuit theory (e.g, ECE 2300)
electronics
power engineering
magnetics
ECE 2317
Examples of high-frequency systems that are not modeled by statics:
antennas
transmission lines
microwaves
optics
ECE 3317

6. Charge Ben Franklin electron: q = e = -1.602 x 10-19 [C]
proton: q = -e = x [C]
1 [C] = 1 / x protons
= x 1018 protons
atom e p
Ben Franklin

7. Charge Density v V Q 1) Volume charge density v [C/m3]
uniform cloud of charge density

8. Charge Density (cont.) dV dQ
non-uniform (inhomogeneous) volume charge density
v (x,y,z) dV dQ
non-uniform cloud of charge density

9. Charge Density (cont.) so
v (x,y,z) dV dQ or

10. Charge Density (cont.) S Q 2) Surface charge density s [C/m2]
s (x,y,z) S
non-uniform sheet of charge density Q
non-uniform
uniform

11. Charge Density (cont.)
s (x,y,z) dQ dS

12. Charge Density (cont.) l + Q 3) Line charge density l [C/m]
l (x,y,z) Q l +
non-uniform line charge density
non-uniform
uniform

13. Charge Density (cont.)
l (x,y,z) dQ dl +

14. Example – Find the total charge in the spherical distributionz
v = 10 [C/m3] a y x
Find: Q

15. Example – Find the total charge
in the non-uniform spherical distribution z
v = 2r [C/m3] a y r
Find: Q x

16. Example – Find the Equivalent Surface Charge Density for a Thin Slab of Chargez

17. Example – Find the Equivalent Line Charge Density for a Thin Cylinder of Chargez

18. Summary of Conversion to Equivalent Charge Densities
Slab lying in a constant z-plane:
Cylinder lying parallel to the z-axis: